Orthogonal versus efficient design

[ELC]

Hi,

I am preparing an experimental plan using Ngene for the first time.
Alternatives are unlabelled. 2 alternatives have the same attributes and levels. Alternative 3 is an opt out option.
I suspect interactions between some of the attributes.
I have very limited information on priors. Some attributes have been researched in the literature but not all, and in a very different context.
Most attributes (all but price) are qualitative, with up to 4 levels.
I am planning to use a latent class model, as - based on about 75 semi-structured interviews - I suspect significant heterogeneity in preferences. For some variables, parameters may even have different signs across classes.
At this stage, I could still decide to simplify the design if needed, but I am not sure if time and budget will allow to run a pilot.

I have been trying 2 syntax, but I am not sure what choice would be best, & if it can be improved with limited knowledge (if any) on priors.

? Orthogonal design 4x4x2x2x6 with 2 ways interactions X1*X2 and X2*X3
Design
; alts = alt1, alt2, alt3
; rows = 36
; block = 4
; orth=seq
; model:
U(alt1)=b1 * x1[0,1,2,3] + b2 * x2[0,1,2,3] + b3 * x3[0,1] + b4* x4[0,1] + b5 * x5[0,1,2,3,4,5] + b6 * x1 * x2 + b7 * x2 * x3 /
U(alt2)=b1 * x1 + b2 * x2 + b3 * x3 + b4 * x4 + b5 * x5 + b6 * x1 * x2 + b7 * x2 * x3 $


? Efficient design 4x4x2x2x6 with 2 ways interactions X1*X2 and X2*X3
Design
; alts = alt1, alt2, alt3
; rows = 24
; block = 4
; eff=(mnl,d)
; model:
U(alt1)=b1 * x1[0,1,2,3] + b2 [0.0001]* x2[0,1,2,3] + b3 * x3[0,1] + b4[0.0001]* x4[0,1] + b5[0.0001] * x5[0,1,2,3,4,5] + b6 * x1 * x2 + b7 * x2 * x3 /
U(alt2)=b1 * x1 + b2 * x2 + b3 * x3 + b4 * x4 + b5 * x5 + b6 * x1 * x2 + b7 * x2 * x3 $

Remark: b1 and b3 are parameters which sign might change across classes.

All variables are qualitative, except for x5 (price). So, I was also wondering if using .effect[...] makes sense with no prior; and if I can use .effect for some variables (that I suspect to have an important weight on utility) but not others.

In addition, I assume that it does not make sense to use priors derived from the literature for 2 parameters but not others unless I can develop an expert guess for the others, I would be glad to get confirmation. I understand that I can have some priors at zero and others very small (when I have the sign), and that it would be better to assume zero or minimal priors rather than make a very partially informed guess.

Thanks in advance for any help or advice you could provide.

[Michiel Bliemer]

(Apologies for the late reply, I am currently on leave)

I would opt for an efficient design with zero priors. Efficient designs give you much more flexibility (and they will be close to orthogonal when you use zero priors). Since you are not checking for dominance, there is no need to know the sign of the parameters, so you can simply use zeros for all. It is fine to have some effects coded, and to have others simply linearly coded. Just use the coding that you will most likely be using in model estimation. If unsure, you can perhaps effects code all variables, as this is the most complex model. You can also add interactions between effects coded variables.

[Michiel Bliemer]

And regarding having information on some priors and not all, I am inclined to say that any information is good to add, however, it also means that attributes with a non-zero prior will become more important in the utility specification, and this can mean that Ngene does not put as much focus on obtaining information from attributes with a zero prior. Therefore, if you add prior information, be conservative to choose values not too far from zero such that you do not implicitly say that the other attributes are not so important.